The thermostatistical aspect of Werner-type states and quantum entanglement

A general Werner-type state is studied from two viewpoints: (i) an application of dynamical interaction of the objective system with its environment, represented by a unital positive operator-valued measure (POVM), which ensures increase of entropy, makes the system evolve from an initial pure state to a mixed state of the Werner type, and (ii) the space of the objective system is constrained to have a given value of the fidelity. Then, the maximum entropy principle is shown to yield the Werner-type state as a canonical ensemble with the projector Hamiltonian. This novel observation is illustrated by examples of bipartite systems, the separability criteria on which are given in terms of the values of temperature. The present viewpoint may cast light on relevance of thermostatistics to the physics of quantum entanglement. In addition, the POVM scheme presented here offers a way of experimentally generating the Werner-type thermal states.